I found a solution using SOCKS to route traffic from specific applications to a specific interface:
1. Install dante-server on the server to provide a SOCKS server.
2. Add a default gateway for the second ISP connection (e.g., "route add default gw 192.168.1.1 dev eth1" if the second ISP is connected at eth1 with a LAN on 192.168.1.0/255.255.255.0 and a gateway on 192.168.1.1).
3. Configure danted.conf to route traffic from clients on eth0 to the second ISP on eth1:
4. Configure applications to connect via the SOCKS server in those cases where the applications should use the second ISP.
internal: eth0 port = 1080
internal: 127.0.0.1 port = 1080
5. Client applications that don't have a SOCKS setting may be socksified using tsocks, whose /etc/tsocks.conf file should have the following lines appended:
server = your.server.ip.address
server_type = 5
server_port = 1080